Question

Under what conditions will the vectors $\overrightarrow{A}=3\hat{i}-5\hat{j}+5\hat{k}and5\hat{i}-\hat{j}+b\hat{k}$ be perpendicular to each other?
Find the value of |b|?

Answer 1

The condition of two vectors are to be perpendicular to each other if dot product of two vectors is zero. i.e, $\overrightarrow{A}.\overrightarrow{B}=0$

or $(3\hat{i}-5\hat{j}+5\hat{k}).(5\hat{i}-\hat{j}+b\hat{k})=0$

or $15+5+5b=0$

or $b=-4$ or $|b|=|-4|=4$